Cooling is one of the most important technical

challenges facing many diverse industries, including

microelectronics, transportation, solid-state lighting,

and manufacturing. Technological developments such

as microelectronic devices with smaller (sub-100 nm)

features and faster (multi-gigahertz) operating

speeds, higher-power engines, and brighter optical

devices are driving increased thermal loads, requiring

advances in cooling. The conventional method for

increasing heat dissipation is to increase the area

available for exchanging heat with a heat transfer

fluid. However, this approach requires an undesirable

increase in the thermal management system’s size.

There is therefore an urgent need for new and

innovative coolants with improved performance. The

novel concept of ‘nanofluids’ – heat transfer fluids

containing suspensions of nanoparticles – has been

proposed as a means of meeting these challenges1.

Nanofluids are solid-liquid composite materials consisting

of solid nanoparticles or nanofibers with sizes typically of

1-100 nm suspended in liquid. Nanofluids have attracted

great interest recently because of reports of greatly

enhanced thermal properties. For example, a small amount

(<1% volume fraction) of Cu nanoparticles or carbon

nanotubes dispersed in ethylene glycol or oil is reported to

increase the inherently poor thermal conductivity of the

liquid by 40% and 150%, respectively2,3. Conventional

particle-liquid suspensions require high concentrations

(>10%) of particles to achieve such enhancement. However,

by Pawel Keblinski1, Jeffrey A. Eastman2, and David G. Cahill3

Nanofluids for thermal transport

1Materials Science and Engineering Department,

Rensselaer Polytechnic Institute, 110 8th St., MRC115,

Troy, NY 12180, USA

E-mail: keblip@rpi.edu

2Materials Science Division, Argonne National

Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA

E-mail: jeastman@anl.gov

3Department of Materials Science and Engineering,

and Frederick Seitz Materials Research Laboratory,

University of Illinois, Urbana-Champaign,

1304 W. Green St., USA

E-mail: d-cahill@uiuc.edu

June 200536 ISSN:1369 7021 © Elsevier Ltd 2005

Nanofluids, i.e. fluid suspensions of nanometer-sized

solid particles and fibers, have been proposed as a

route for surpassing the performance of heat transfer

liquids currently available. Recent experiments on

nanofluids have indicated significant increases in

thermal conductivity compared with liquids without

nanoparticles or larger particles, strong temperature

dependence of thermal conductivity, and significant

increases in critical heat flux in boiling heat transfer.

Some of the experimental results are controversial,

e.g. the extent of thermal conductivity enhancement

sometimes greatly exceeds the predictions of well-

established theories. So, if these exciting results on

nanofluids can be confirmed in future systematic

experiments, new theoretical descriptions may be

needed to account properly for the unique features of

nanofluids, such as high particle mobility and large

surface-to-volume ratio.

REVIEW FEATURE

problems of rheology and stability are amplified at high

concentrations, precluding the widespread use of

conventional slurries as heat transfer fluids. In some cases,

the observed enhancement in thermal conductivity of

nanofluids is orders of magnitude larger than predicted by

well-established theories. Other perplexing results in this

rapidly evolving field include a surprisingly strong

temperature dependence of the thermal conductivity4,5 and a

three-fold higher critical heat flux compared with the base

fluids6,7.

These enhanced thermal properties are not merely of

academic interest. If confirmed and found consistent, they

would make nanofluids promising for applications in thermal

management. Furthermore, suspensions of metal

nanoparticles are also being developed for other purposes,

such as medical applications including cancer therapy8. The

interdisciplinary nature of nanofluid research presents a great

opportunity for exploration and discovery at the frontiers of

nanotechnology9.

Synthesis of nanofluidsThe optimization of nanofluid thermal properties requires

successful synthesis procedures for creating stable

suspensions of nanoparticles in liquids. Depending on the

requirements of a particular application, many combinations

of particle materials and fluids are of potential interest. For

example, nanoparticles of oxides, nitrides, metals, metal

carbides, and nonmetals with or without surfactant molecules

can be dispersed into fluids such as water, ethylene glycol, or

oils. Studies to date have used one or more of several

possible methods for nanoparticle production and dispersion.

Here, we briefly mention the techniques that, so far, have

been most commonly used.

Several studies, including the earliest investigations of

nanofluids, used a two-step process10 in which nanoparticles

or nanotubes are first produced as a dry powder, often by

inert gas condensation11 (Fig.1, middle). Chemical vapor

deposition has also been used to produce materials for use in

nanofluids, particularly multiwalled carbon nanotubes3. The

nanoparticles or nanotubes are then dispersed into a fluid in

a second processing step. Simple techniques such as

ultrasonic agitation or the addition of surfactants to the

fluids are sometimes used to minimize particle aggregation

and improve dispersion behavior. Such a two-step process

works well in some cases, such as nanofluids consisting of

oxide nanoparticles dispersed in deionized water10. Less

success has been found when producing nanofluids

containing heavier metallic nanoparticles12. Since

nanopowder synthesis techniques have already been scaled

up to industrial production levels by several companies13,

there are potential economic advantages in using two-step

synthesis methods that rely on the use of such powders.

Single-step nanofluid processing methods have also been

developed. For example, nanofluids containing dispersed

metal nanoparticles2,11 have been produced by a ‘direct-

evaporation’ technique14 (Fig. 1, left). As with the inert gas

condensation technique, this involves the vaporization of a

source material under vacuum conditions. An advantage of

this technique is that nanoparticle agglomeration is

minimized, while a disadvantage is that only low vapor

pressure fluids are compatible with the process. Various

single-step chemical synthesis techniques can also be

employed to produce nanofluids. For example, a technique

developed by Brust and coworkers15 for producing metallic

nanoparticles by the reduction of metal salts has been used

widely to produce colloidal suspensions in various solvents

June 2005 37

Fig. 1 Transmission electron micrographs showing (left) Cu nanofluids2 (© 2001 American Institute of Physics), (middle) CuO nanoparticles10 (© 1999 MRS), and (right) alkanethiol

terminated AuPd colloidal particles16 (© 2002 American Physical Society) used in studies of interfacial resistance. CuO particles show significant clustering associated with synthesis

techniques and subsequent agglomeration. AuPd colloids show the best dispersion and very narrow size distribution.

for a wide range of applications, including studies of thermal

transport16 (Fig. 1, right). Excellent control of size and very

narrow size distributions can be obtained by using such

methods.

Thermal transport in stationary fluidsKey features of nanofluids that have been reported so far

include thermal conductivities exceeding those of traditional

solid/liquid suspensions2,3; a nonlinear relationship between

thermal conductivity and concentration in the case of

nanofluids containing carbon nanotubes3; strongly

temperature-dependent thermal conductivity4; and a

significant increase in critical heat flux in boiling heat

transfer6,7,17. Each of these features is highly desirable for

thermal systems; a stable and easily synthesized fluid with

these attributes and acceptable viscosity would be a strong

candidate for the next generation of liquid coolants.

Published reports of how the thermal conductivity of the

nanofluid varies as a function of nanoparticle loading are

summarized in Fig. 2. Early experimental studies of the

thermal transport properties of nanofluids focused on

changes in properties created by high concentrations of oxide

nanoparticles. Masuda et al.18 reported a 30% increase in the

thermal conductivity of water with the addition of 4.3 vol.%

Al2O3 nanoparticles. A subsequent study by Lee et al.10 also

examined the behavior of Al2O3 nanoparticles in water, but

observed only a 15% enhancement in thermal conductivity at

the same nanoparticle loading. These differences in behavior

were attributed to differences in average particle size in the

two sets of samples. The Al2O3 nanoparticles used by Masuda

et al. had an average diameter of 13 nm, compared with

33 nm in the study by Lee et al. Xie and coworkers19,20 found

an intermediate result, i.e. the thermal conductivity of water

is enhanced by approximately 20% by a nanoparticle loading

of 5 vol.%. The same group found similar results for SiC21.

Lee et al. observed only a modest improvement in the thermal

conductivity of nanofluids containing CuO compared with

Al2O3, but Wang and coworkers22 reported a surprising 17%

increase in thermal conductivity for a loading of just 0.4 vol.%

CuO nanoparticles in water. The thermal conductivity of an

ethylene glycol-based nanofluid was shown2 to be increased

by up to 40% when loaded with approximately 0.3 vol.% Cu

nanoparticles of mean diameter ~10 nm. Patel and

coworkers5 observed increases in fluid thermal conductivity

of up to 21% in their recent study on the behavior of Au and

Ag nanoparticles dispersed in water and toluene, but,

astonishingly, were able to achieve these results at extremely

low nanoparticle loadings of just 0.011 vol.%.

To the best of our knowledge, the anomalously large

increases in thermal conductivity observed for CuO

nanofluids22, Cu nanofluids2, and Au and Ag nanofluids5 have

not been confirmed independently. In fact, a recent attempt

at duplicating the Cu nanofluid results2 appears to have

failed: in this case, the Cu nanoparticles were larger (50 nm)

but no significant enhancement in thermal conductivity was

observed with Cu nanoparticle loadings of up to 0.5 vol.%23.

A potentially important development is the recent

observation of a strong temperature dependence of

enhancement in thermal conductivity for both high

concentrations of oxide nanoparticles4 and extremely low

concentrations of metal nanoparticles5. In both nanofluid

systems, a two- to four-fold increase in the enhancement of

thermal conductivity was observed over a small temperature

range (20-50°C). If confirmed, and if this temperature

dependence occurs over a wide temperature range, then this

property could make nanofluids particularly attractive for

applications at elevated temperatures.

The largest increases in thermal conductivity have been

observed in suspensions of carbon nanotubes, which, in

addition to high thermal conductivity, have very high aspect

ratio (Fig. 3). Since carbon nanotubes form a highly entangled

REVIEW FEATURE

June 200538

Fig. 2 Relative increase in the thermal conductivity as a function of the volume fraction of

nanoparticles2,4,5,10,19,21,23,45. The lower dashed line is the prediction from effective

medium theory for well-dispersed suspensions of highly thermally conductive

nanoparticles; the upper dashed line is the prediction for random-close-packed

aggregates of nanoparticles. Most of the data is reasonably well described by effective

medium theory. The most anomalous results (furthest left and above the dashed lines) for

Cu and Au nanoparticle suspensions are2,45, respectively.

REVIEW FEATURE

fiber network, they are not mobile, as demonstrated by

viscosity measurements24, and thus their effect on the

thermal transport of fluid suspensions is expected to be

similar to that of polymer composites. The first reported

work on a single-walled carbon nanotube-polymer epoxy

composite, by Biercuk et al.25 (Fig. 3a), demonstrated a 125%

increase in thermal conductivity at 1 wt.% nanotube loading

at room temperature. Biercuk et al. also observed a thermal

conductivity that increases with increasing temperature. Choi

et al.3 measured thermal conductivities of oil suspensions

containing multiwalled carbon nanotubes (Fig. 3b) up to

1 vol.% loading and found similar behavior, in this case a

160% enhancement. Interestingly, the conductivity

enhancement increased more rapidly than a linear

dependence on nanotube loading. Thus, interactions of

thermal fields associated with different fibers may become

important as the loading approaches 1 vol.%.

Several studies of carbon nanotube suspensions have

shown smaller enhancements in thermal conductivity: Xie

et al.26 measured carbon nanotube-organic liquid and water

suspensions and found only 10-20% increases in thermal

conductivity at 1 vol.%; Wen and Ding27 found a ~25%

enhancement in the conductivity at ~ 0.8 vol.% carbon

nanotubes in water; and Assael and coworkers23 found a

maximum enhancement of 38% with 0.6 vol.% nanotubes in

water. In Wen and Ding’s work, the enhancement in the

conductivity of the suspension increases rapidly with loading

up to 0.2 vol.% and then begins to saturate. In agreement

with Biercuk et al.25, Wen and Ding observed increases in

thermal conductivity with increasing temperature. However,

these increases tended to saturate at T > 30°C.

Flow, convection, and boilingRecently, the heat transfer coefficient of nanofluids in

natural28,29 and forced flow30-32 has been measured. Also,

Das et al.17 initiated experiments on the boiling

characteristics of nanofluids. You et al.6 measured the critical

heat flux in a pool of boiling Al2O3-water nanofluid and

reported an unprecedented three-fold increase over that of

pure water. Subsequently, Vassallo et al.7 reported that silica-

water nanofluid shows three-fold higher critical heat flux

compared with base fluids.

In convective heat transfer in nanofluids, the heat transfer

coefficient depends not only on the thermal conductivity but

also on other properties, such as the specific heat, density,

and dynamic viscosity of a nanofluid. At low volume

fractions, the density and specific heat of nanofluids are

expected, and have been observed33, to be very similar to

those characterizing the base fluid. Wang et al.34 measured

the viscosity of Al2O3-water nanofluids and showed that

nanofluids have lower viscosities when the particles are more

dispersed. They also found an increase of ~30% in viscosity

at 3 vol.% Al2O3, compared with that of water alone.

However, the viscosity of the Al2O3-water nanofluid prepared

by Pak and Cho35 was three times higher than that of water.

As expected, the viscosity of nanofluids depends on the

methods used to disperse and stabilize the nanoparticle

suspension. Xuan and Li32 measured the turbulent friction

factor of water-based nanofluids containing Cu nanoparticles

in a volume fraction range of 1.0-2.0. Interestingly, they

found that the friction factor for the nanofluids is

approximately the same as that of water.

Forced convection measurements by Eastman et al.36

reported that the heat transfer coefficient of water

containing 0.9 vol.% of CuO nanoparticles was improved by

>15% compared with that of water without nanoparticles.

Xuan and Li32 measured the convective heat transfer

coefficient and friction factor of Cu-water nanofluids in

turbulent flow. Their results show that a small amount

(<2 vol.%) of Cu nanoparticles in deionized water improves

Fig. 3 Scanning electron micrographs of carbon nanotube samples typical of those used in suspensions and composites: (a) single-walled carbon nanotubes obtained by arc discharge and

(b) multiwalled carbon nanotubes obtained by chemical vapor deposition growth. (Courtesy of P. M. Ajayan, Rensselaer Polytechnic Institute.)

June 2005 39

convective heat transfer remarkably. For example, the

convective heat transfer coefficient of a nanofluid containing

2.0 vol.% of Cu nanoparticles was improved by >39%

compared with that of water without nanoparticles. In

contrast to these studies, Pak and Cho35 found that the

convective heat transfer coefficient of water-based

nanofluids with 3 vol.% Al2O3 and TiO2 nanoparticles was

12% smaller than that of pure water when tested under the

condition of constant average velocity. Putra et al.28 studied

natural convection of Al2O3- and CuO-water nanofluids.

Unlike conduction or forced convection, these natural

convection experiments show a decrease in heat transfer.

The pool boiling experiments of Das et al.17 on Al2O3-

water nanofluids showed a deterioration of the pool boiling

performance of nanofluids with increasing particle volume

fraction. This deterioration is not attributed to a change in

fluid properties by nanoparticles, but to a change in the

boiler’s surface characteristics by nanoparticles deposited on

the rough surface of the boiler. You et al.6 measured the

critical heat flux in pool boiling on a flat, square Cu surface

immersed in Al2O3-water nanofluids and showed an

unprecedented three-fold increase in critical heat flux over

that of pure water. The average size of the departing bubbles

increases and the bubble frequency decreases significantly in

nanofluids compared with pure water. The remarkable results

of You et al.6 are consistent with the more recent results of

Vassallo et al.7, who conducted experiments with silica-water

nanofluids. It is intriguing that nanoparticles at

concentrations as low as 10-3 vol.% can trigger such a

dramatic increase in critical heat flux; no existing model can

explain such an effect.

Thermal conductivity of nanofluids:understanding and controversySince studies of nanofluid thermal conductivity have been

more prevalent than studies of other heat transfer properties,

we limit our discussion to thermal conductivity, i.e. heat

transfer by conduction in stationary fluids. Nanofluids are

composite materials and, therefore, any discussion of

nanofluid thermal conductivity must begin with effective

medium theories. Effective medium theories were introduced

by Mossotti, Clausius, Maxwell, and Lorenz in the late 19th

century, firmly established with the work of Bruggeman37,

and thoroughly investigated and applied in many fields of

science and engineering since then38.

We begin our discussion with the simplest case of

spherical particles where interface effects are negligible. In

other words, at this stage we do not consider the finite

thermal conductance of the particle/fluid interface. In the

limit of a small volume fraction of nanoparticles f all versions

of the effective medium theory converge to the same

solution and, in the limit of high thermal conductivity

particles, predict that the nanofluid’s thermal conductivity

enhancement will be 3f. This prediction is a good

approximation to the exact solution for finite thermal

conductivity particles, as long as the thermal conductivity of

the particle is >20 times the thermal conductivity of the

fluid39. As shown in Fig. 2, many experimental results on

nanofluids are in reasonably good agreement with this

prediction, e.g. the 26 nm SiC nanofluids and alumina-water

nanofluids studied by Xie and coworkers21 and the alumina-

ethylene glycol nanofluids studied by Lee10. As we discuss

below, the interface resistance between the nanoparticle and

surrounding fluid will reduce the predictions of the effective

medium theory. For particles on the order of 30 nm in

diameter, however, we do not expect the reduction to be

significant.

Many of the other results for high concentrations of

nanoparticles can also be understood based on effective

medium theory, if we allow for the possibility that the

nanoparticles have clustered into small aggregates (Fig. 1,

middle). Since an aggregate of nanoparticles occupies more

space than the individual nanoparticles that make up the

aggregate, the volume fraction of the aggregates is larger

than the volume fraction of nanoparticles40. A random close

packing of spherical nanoparticles will have a relative density

of approximately 60%. So, if the nanoparticles have

aggregated, we can expect an enhancement in the thermal

conductivity of approximately 3f/0.6, or 5f. Even larger

enhancements are possible for more loosely packed clusters

(Fig. 4). An enhancement in the thermal conductivity of

approximately 5f is often observed20. The thermal

conductivity of the aggregate will, of course, be smaller than

the thermal conductivity of the nanoparticle, but this

reduction in conductivity – we estimate a factor of two

reduction in thermal conductivity of the aggregate relative to

the nanoparticle – will not be a significant factor if the

conductivity of the nanoparticles is sufficiently large.

Effective medium theories for fiber composites are more

complex, but the equations can be solved exactly for a high-

REVIEW FEATURE

June 200540

REVIEW FEATURE

aspect-ratio ellipsoid. As before, the predictions of effective

medium theories converge to a common solution in the limit

of a small volume fraction f. In this case, however, knowledge

of the thermal conductivity and aspect ratio of the fiber are

needed to make quantitative predictions for the thermal

conductivity of the composite. For example, in the limit of

high-aspect-ratio fibers, a simple geometrical analysis

provides an estimate for the composite thermal conductivity

Λeff, assuming that the thermal resistance of the nanotube

interfaces is negligible:

Λeff = f Λfiber <cos2 θ> (1)

where Λeff and Λfiber are the thermal conductivity of the

composite and fiber, respectively, f is the fiber volume

fraction, and θ is the angle between the direction of heat

flow and the fiber axis. The brackets in eq 1 indicate an

average over all fibers in the composite. Even for random fiber

orientations (<cos2 θ> = 1/3) with Λfiber =3000 W/m K,

f = 0.01, eq 1 yields Λeff = 10 W/m K, which is ~15 times

larger than the conductivity of water and ~50 times larger

than the conductivity of an organic liquid. If realizable,

nanofluids containing such fibers would have obvious

technological applications. However, the largest

enhancements observed by experiment have been about

factor of two.

This lower-than-expected thermal conductivity is

attributed to the thermal interfacial resistance Rk. The

interfacial conductance G = 1/Rk is related to the heat flux JQ

and the temperature drop at the interface ∆T via:

JQ = G ∆T . (2)

A simple measure of the relative importance of interfacial

resistance in the overall heat flow in a composite can be

obtained from the equivalent thickness h, defined as the

distance over which the temperature drop is the same as at

the interface. This thickness is given by the ratio of fluid

thermal conductivity Λ to the interfacial conductance,

h = Λ/G.

The interfacial resistance between a nanotube and an

organic material was recently determined via a combination

of laser-heating experiments and molecular simulations41. In

the experiment, an interfacial conductance of 12 MW/m2K

was measured, and similar results were obtained from

molecular dynamics simulations (Fig. 5). The equivalent

matrix thickness for a low-conductivity organic matrix

(~0.1 W/m K) for the above values of interfacial resistance is

about 10 nm. This is indeed a large value. For example, two

tubes separated by 1 nm of matrix material will be separated

thermally to a degree equivalent to a layer of the matrix

material that is 20 nm thick. Furthermore, even if tubes are in

direct contact, they only interact with weak dispersion forces

Fig. 5 Snapshot of atomic positions of a carbon nanotube immersed in liquid octane.

Molecular dynamics simulations show that weak van der Waals forces acting between the

nanotube and the liquid provide only poor thermal coupling and, consequently, the

interfacial resistance to the heat flow is very significant.

June 2005 41

Fig. 4 Predictions from effective medium theory of the composite conductivity normalized

by the conductivity of the matrix as a function of volume fraction f loading of high thermal

conductivity spherical nanoparticles: solid squares – well-dispersed particles; circles –

clusters of packed particles (60 vol.% particles); open squares – loosely packed clusters

(40 vol.% particles).

and are expected to experience a large tube-tube contact

resistance. The fact that both tube-matrix interface

resistance and tube-tube contact resistance are large explains

the lack of a percolation threshold in thermal transport25.

The effects of the interface thermal resistance can be

included in effective medium theories42,43. The effective

thermal conductivity as a function of the fiber aspect ratio

for a typical carbon nanotube is shown in Fig. 6. When the

aspect ratio is ~3000 we recover the full thermal

conductivity enhancement predicted by eq 1. However,

carbon nanotubes have lower aspect ratios. Also, in a

suspension or composite, nanotubes are curved9 (Fig. 3),

which further reduces their effective aspect ratio. The critical

aspect ratio, α , needed to recover the prediction of eq 1

scales as:

αcritical ~ √Λfiber/G r (3)

where r is the fiber radius and G is the fiber-matrix interfacial

conductance.

The interfacial thermal resistance also has an effect on

spherical particle composites. In this case, in the limit of low

volume fractions of nanoparticles, effective medium theory39

predicts:

Λeff /Λmatrix - 1 = 3f (γ-1)/(γ+2) (4)

where γ is the ratio of the particle radius to the equivalent

matrix thickness h.

According to eq 4, when the particle radius becomes equal

to the equivalent matrix thickness (γ = 1), there is no

enhancement at all; for larger interfacial resistance (γ < 1),

the addition of particles decreases the thermal conductivity

of the composite. The thermal conductance of particle/matrix

interfaces has also been measured recently: alumina particles

in polymethyl methacrylate (PMMA) give G = 30 MW/m2K;

Au alloy particles stabilized by alkane-thiol chemistries and

suspended in toluene give G = 15 MW/m2K; and Au alloy

particles stabilized by a variety of surfactants and suspended

in water give 150 < G < 250 MW/m2K (Fig. 1, right)16,39,44.

Evaluation of eq 3 is complicated by two factors: the

correct choice for average particle radius and the correct

choice of interface thermal conductance G. Typically, authors

report the number-weighted average of the particle radius.

But in eq 3, we must use the volume-weighted average of the

particle radius39. If the polydispersity is large, then the

volume-weighted average radius will be significantly larger

than the average radius. As reviewed above, the thermal

conductance of particle-fluid interfaces is known in only a few

cases. For example, we are not aware of any measurement of

the thermal conductance of interfaces between oxide particles

and fluids. Nevertheless, if we take G = 200 MW/m2K as a

typical value of the conductance of a particle-water interface

and use a volume-weighted average radius of 30 nm, then

γ = 10 and the effective medium prediction for the

enhancement of the thermal conductivity by 3f will not be

significantly decreased by the interface effects.

Thermal motion of nanoparticles has sometimes been

proposed as a mechanism that could enhance the thermal

conductivity of a nanofluid. For Brownian motion to be a

significant contributor to the thermal conductivity, it would

have to be a more efficient heat-transfer mechanism than

thermal diffusion in the fluid. However, Keblinski et al.40,

using a simple analysis, have shown that thermal diffusion is

much faster than Brownian diffusion, even within the limits

of extremely small particles. In other words, thermal fields

adjust to instantaneous particle positions and act as they do

in an immobile particle composite. A number of other

researchers have reached the opposite conclusion, including:

(i) Xuan and Li32, whose work is hard to assess since their

result for the thermal conductivity enhancement (their eq 13)

has the wrong units; (ii) Kumar et al.45, who postulate that

the Brownian motion mean free path of a nanoparticle in

fluid is on the order of 1 cm, which is unphysical; and

REVIEW FEATURE

June 200542

Fig. 6 The effective composite conductivity estimated from effective medium theory42,

normalized by the conductivity of the matrix and plotted as a function of the fiber aspect

ratio. The interfacial resistance is set equal to the thermal resistance of a layer of the

matrix material that is five times the radius of the fiber. Other parameters are the thermal

conductivity of the fiber, 3000 W/m K, and the thermal conductivity of the matrix,

0.15 W/m K.

REVIEW FEATURE

(iii) Bhattacharya et al.46, who, to obtain agreement with

experiment, introduced an interparticle potential with a range

of the order of one light year in their Brownian dynamics

simulations.

A more recent idea relating to Brownian motion, put

forward by Jang and Choi47 and Prasher et al.48, postulates

the importance of the Brownian-motion-driven convection in

the fluid, rather than the direct contribution to the thermal

conductivity of the particle motion itself.

Keblinski et al.40 have put forward other ideas to explain

large thermal conductivity enhancements, including the

possibility of larger thermal conductivity of an ordered liquid

layer at particle interfaces and ‘tunneling’ of heat-carrying

phonons from one particle to another. The same group of

authors, in their subsequent simulation work, conclude that

these mechanisms do not contribute significantly to heat

transfer49. Furthermore, interpretation of the cooling rates of

Au nanoparticles suspended in water and organic solvents do

not appear to require unusual thermophysical properties of

the surrounding liquid to explain the experimental results16.

Outlook and future challenges Many interesting properties of nanofluids have been reported

in the past ten years. Thermal conductivity has received the

most attention, but several groups have recently initiated

studies of other heat-transfer properties. The use of

nanofluids in a wide variety of applications appears

promising, but the development of the field is hindered by:

(i) the lack of agreement between results obtained in

different laboratories; (ii) the often poor characterization of

the suspensions; and (iii) the lack of theoretical

understanding of the mechanisms responsible for the

observed changes in properties. We conclude by outlining

several important issues that we believe should receive

greater attention in the future.

• Stability of the suspension is a crucial issue for both

scientific research and practical applications. Particle

aggregation and the formation of extended structures of

linked nanoparticles may be responsible for much of the

disagreement between experimental results and the

predictions of effective medium theory. Simultaneous

studies of thermal conductivity and viscosity may give

additional insight. Some aggregation may be beneficial for

suspensions of spherical nanoparticles, but, for nanotube

suspensions and composites, aggregation is detrimental

since bundling of nanotubes reduces the fiber aspect ratio.

• The size distribution of nanoparticles and nanoparticle

aggregates in the suspensions is rarely reported. This lack

of data can be attributed to the difficulty in properly

characterizing high-concentration suspensions of

nanoparticles, e.g. light scattering techniques work poorly

or not at all at the high particle concentrations usually

under consideration in nanofluid research. Cryogenic

transmission electron microscopy might provide a powerful

characterization method, but few materials laboratories

are equipped to apply this technique and the structure of

the nanofluids may change during cryofixation.

• In most studies to date, sample sizes have been limited to

less than a few hundred milliliters of nanofluid. Larger

June 2005 43

Fig. 7 (top) Interfacial resistance between a carbon nanotube and liquid octane in units of

equivalent matrix thickness plotted as a function of the fraction of nanotube carbon

atoms with covalently attached octane molecules. Results were obtained from molecular

dynamics simulations50. The inset shows a functionalized carbon nanotube. (bottom)

Axial conductivity of the carbon nanotube versus the fraction of functionalized nanotube

carbon atoms.

samples will be needed to test many properties of

nanofluids in the future, particularly in assessing their

potential for use in applications. Inert gas condensation

synthesis, which has already been scaled up to produce

large quantities of nanopowders, typically produces

heavily agglomerated powders. Robust techniques for

large-scale production of stable nanofluids are needed.

• High interfacial thermal resistance appears to be a critical

factor in reducing the benefits of carbon nanotube fillers.

Surface modification or functionalization may lead to

stronger thermal conductivity enhancements. Scattering of

thermal waves (phonons) by defects in tube crystal

structure will, however, limit the benefit of the

functionalization50 by reducing the intrinsic thermal

conductivity of the nanotubes (Fig. 7).

• Large increases in the critical heat flux in boiling heat

transfer have been reported within the past year, and this

phenomenon deserves thorough study. Thermal

conductivity is probably not a critical issue for critical heat

flux6, but the mechanisms that produce the increases are

unknown at this time.

• Several studies have revealed significant increases in the

heat transfer coefficient under forced flow conditions and

in pool boiling experiments. However, other studies have

yielded decreases in the heat transfer coefficient because

of the addition of nanoparticles to the fluid. Heat transfer

under forced flow conditions is most relevant regarding

applications, so it is important to systematically identify

factors leading to enhancement or deterioration of these

convective heat flow characteristics. MT

AcknowledgmentsThis work was supported by the US Department of Energy (DOE), Basic Energy Sciences-

Materials Sciences, under contract no. W-31-109-ENG-38, and DOE grants DEFG02-

01ER45938 and DE-FG02-04ER46104. We thank Yee Kan Koh for help in preparing Fig. 2.

REVIEW FEATURE

June 200544

REFERENCES

1. Choi, S. U. S., Enhancing Thermal Conductivity of Fluids with Nanoparticles. In:

Developments and Applications of Non-Newtonian Flows, Singer, D.A., and

Wang, H. P., (eds.), American Society of Mechanical Engineers, New York,

(1995), 99

2. Eastman, J. A., et al., Appl. Phys. Lett. (2001) 78 (6), 718

3. Choi, S. U. S., et al., Appl. Phys. Lett. (2001) 79 (14), 2252

4. Das, S. K., et al., J. Heat Trans. (2003) 125 (4), 567

5. Patel, H. E., et al., Appl. Phys. Lett. (2003) 83 (14), 2931

6. You, S. M., et al., Appl. Phys. Lett. (2003) 83 (14), 3374

7. Vassallo, P., et al., Int. J. Heat Mass Trans. (2004) 47, 407

8. O’Neal, D. P., et al., Cancer Lett. (2004) 109 (2), 181

9. See, for example: Ajayan, P. M., et al., Nanocomposite Science and Technology,

Wiley-VCH, (2003)

10. Lee, S., et al., J. Heat Trans. (1999) 121 (2), 280

11. Granqvist, C. G., and Buhrman, R. A., J. Appl. Phys. (1976) 47 (5), 2200

12. Eastman, J. A., et al., In Nanocrystalline and Nanocomposite Materials II,

Komarneni, S., et al., (eds.), Materials Research Society, Pittsburgh, (1997), 3

13. Romano, J. M., et al., Adv. Powder Metall. Partic. Mater. (1997) 2, 12

14. Yatsuya, S., et al., J. Cryst. Growth (1978) 43, 490

15. Brust, M., et al., J. Chem. Soc., Chem. Commun. (1994) (7), 801

16. Wilson, O. M., et al., Phys. Rev. B (2002) 66, 224301

17. Das, S. K., et al., Int. J. Heat Mass Trans. (2003) 46, 851

18. Masuda, H., et al., Netsu Bussei (Japan) (1993) 4, 227

19. Xie, H., et al., J. Appl. Phys. (2002) 91 (7), 4586

20. Xie, H., et al., Mater. Sci. Lett. (2002) 21 (19), 1469

21. Xie, H., et al., Int. J. Thermophys. (2002) 23 (2), 571

22. Zhou, L. P., and Wang, B. X., Annu. Proc. Chinese Eng. Thermophys. (in Chinese)

(2002) 889

23. Assael, M. J., et al., In Thermal Conductivity 27/Thermal Expansion 15: Proc. 27th

Int. Thermal Conductivity Conf. and 15th Int. Thermal Expansion Symp., Wang,

H., and Porter, W. D., (eds.) DEStech Publications, Lancaster, PA, (2005), 153

24. Lin-Gibson, S., et al., Phys. Rev. Lett. (2004) 92 (4), 048302

25. Biercuk, M. J., et al., Appl. Phys. Lett. (2002) 80 (15), 2767

26. Xie, H., et al., J. Appl. Phys. (2003) 94 (8), 4967

27. Wen, D. S., and Ding, Y. L., J. Thermophys. Heat Trans. (2004) 18, 481

28. Putra, N., et al., Heat Mass Trans. (2003) 39, 775

29. Khanafer, K., et al., Int. J. Heat Mass Trans. (2003) 46 (19), 3639

30. Xuan, Y., and Roetzel, W., Int. J. Heat Mass Trans. (2000) 43 (19), 3701

31. Xuan, Y., and Li, Q., Int. J. Heat Fluid Flow (2000) 21, 58

32. Xuan, Y., and Li, Q., J. Heat Trans. (2003) 125, 151

33. Yang, H. S., et al., unpublished

34. Wang, X., et al., J. Thermophys. Heat Trans. (1999) 13, 474

35. Pak, B. C., and Cho, Y. I., Exper. Heat Trans. (1998) 11, 151

36. Eastman, J. A., et al., Mater. Sci. Forum (1999) 312-314, 629

37. Bruggeman, D. A. G., Ann. Phys. (1935) 24, 636

38. Landauer, R., in Electrical Transport and Optical Properties of Inhomogeneous

Media, Garland, J. C., and Tanner, D. B., (eds.), American Institute of Physics,

New York, (1978), 2

39. Putnam, S. A., et al., J. Appl. Phys. (2003) 94 (10), 6785

40. Keblinski, P., et al., Int. J. Heat Mass Trans. (2002) 45 (4), 855

41. Huxtable, S. T., et al., Nat. Mater. (2003) 2 (11), 731

42. Hasselman, D. P. H., and Johnson, L. F., J. Compos. Mater. (1987) 21, 508

43. Nan, C-W., et al., J. Appl. Phys. (1997) 81 (105), 6692

44. Ge, Z., et al., J. Phys. Chem. B (2004) 108, 18870

45. Kumar, D. H., et al., Phys. Rev. Lett. (2004) 93 (14), 144301

46. Bhattacharya, P., et al., J. Appl. Phys. (2004) 95 (11), 6492

47. Jang, S. P., and Choi, S. U. S., Appl. Phys. Lett. (2004) 84 (21), 4316

48. Prasher, R., et al., Phys. Rev. Lett. (2005) 94 (2), 025901

49. Xue, L., et al., Int. J. Heat Mass Trans. (2004) 47 (19-20), 4277

50. Shenogin, S., et al., Appl. Phys. Lett. (2004) 85 (12), 2229